Self-similar solutions to super-critical gKdV

Abstract

We construct self similar finite energy solutions to the slightly super-critical generalized KdV equation. These self similar solutions bifurcate as a function of the exponent $p$ from the soliton at the $L^2$ critical exponent.

References in corpus (1)

• Well-posedness for the supercritical gKdV equation

Cited by in corpus (8)

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• Nonlinear Profile Decomposition and the Concentration Phenomenon for Supercritical Generalized KdV Equations
• Blow-up solutions for $L^2$-supercritical gKdV equations with exactly $k$ blow-up points
• A Spectral Analysis of the Nonlinear Schroedinger Equation in the Co-Exploding Frame
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• A Normal Form for the Onset of Collapse: the Prototypical Example of the Nonlinear Schrodinger Equation